The use of Natural Language Processing (NLP) in the field of law has become a topic of interest in the recent years. Applications to Turkish law, however, have remained unexplored to this day. In this thesis, first, a review of existing NLP applications in law is provided, and then, the problem of predicting Turkish court decisions is studied using NLP techniques. An extensive corpus that consists of case texts from Turkish higher courts, namely, the Constitutional Court and District Courts, is compiled. In addition, a numerical analysis and comparison of NLP methods at predicting the outcomes of these higher court cases is provided. The methods used for prediction are based on Decision Trees, Random Forests, Support Vector Machines and various deep learning models; specifically Gated Recurrent Units, unidirectional and bidirectional Long Short-Term Memory networks, and their attention-integrated counterparts. Prediction results for all algorithms are presented comparatively across all courts. The results show that decisions of Turkish higher courts can be predicted with high accuracy, especially with deep learning-based methods. Similar performance to existing work in the literature on case outcome prediction, which focus on different languages and different legal systems, is achieved.